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This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
PEDMAS |
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associative |
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distributive |
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commutative |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
Find the average of the following numbers: 9, 7, 11, 5.
| 8 | |
| 44 | |
| 13 | |
| 6 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{9 + 7 + 11 + 5}{4} \) = \( \frac{32}{4} \) = 8
Which of the following is not an integer?
1 |
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0 |
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-1 |
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\({1 \over 2}\) |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
What is \( \frac{6}{6} \) - \( \frac{6}{8} \)?
| 1 \( \frac{3}{7} \) | |
| \(\frac{1}{4}\) | |
| 1 \( \frac{5}{13} \) | |
| 2 \( \frac{3}{9} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 4}{6 x 4} \) - \( \frac{6 x 3}{8 x 3} \)
\( \frac{24}{24} \) - \( \frac{18}{24} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{24 - 18}{24} \) = \( \frac{6}{24} \) = \(\frac{1}{4}\)
What is -3y7 + 6y7?
| 3y14 | |
| -9y7 | |
| 3y7 | |
| 3y49 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
-3y7 + 6y7
(-3 + 6)y7
3y7